Prepare for the Punjab Board 2027 Class 8 Mathematics examination with Domain 2: Algebra – Model Paper No. 2. This practice paper is designed to help students understand important algebraic concepts, strengthen problem-solving skills, and prepare effectively according to the new syllabus issued by PECTAA Punjab. Students can use this Class 8 Maths Algebra Model Paper 2027 for revision, self-assessment, and exam preparation. Explore more Punjab Board 2027 Model Papers to improve your confidence and performance in mathematics.
Instructions: Fourty (40) Multiple Choice Questions (MCQs) are given in this part. Each question carries 1 marks.ہدایات: اس حصہ میں چالیس (40) کثیر الانتخابی سوالات دیے گئے ہیں۔ ہر سوال کا 1 نمبر ہے۔
Question No. 1: Multiple Choice Questions.
1.
The point (-1, 2) lies in the quadrant:نقطہ (-1,2) ربع میں ہے۔
(a) I(b) II(c) III(d) IV
Ans: (b) II – x is negative and y is positive, so the point is in the second quadrant.
Quadrants of the plane
2.
Simplification of x2y5xy4 is:x2y5xy4 کی سادہ ترین شکل ہے:
(a) xy(b) y(c)xy(d)xy2
Ans: (a) x2−1 y5−4 = xy.
3.
The coordinates of the origin are:مبدا کے محدودات ہیں:
(a) (1, 1)(b) (1, 0)(c) (0, 1)(d) (0, 0)
Ans: (d) The origin is (0, 0).
4.
Standard form of 6.31 × 10−4 is:6.31 × 10−4 کی معیاری صورت ہے:
(a) 0.000631(b) 0.00631(c) 0.0631(d) 0.631
Ans: (a) Move the decimal point 4 places left: 0.000631.
5.
The value of x = ? when 6x + 4y = 12 and y = 4x کی قیمت کیا ہوگی؟ جبکہ 6x + 4y = 12 اور y = 4
(a)18(b)83(c)−23(d) 4
Ans: (c) 6x + 16 = 12 ⇒ 6x = −4 ⇒ x = −2/3.
6.
If 7x < −14, then:اگر 7x < −14 ہو تو
(a) x > −2(b) x > −12(c) x > 12(d) x < −2
Ans: (d) Divide both sides by 7: x < −2.
7.
The line y = −7x passes through:خط y = −7x ________ میں سے گزرتا ہے:
(a) (0,7)(b) (7,0)(c) (0,0)(d) (7,7)
Ans: (c) Put x = 0: y = 0, so the line passes through the origin.
Sketch of y = −7x (passes through the origin)
8.
If x + y = 6, x − y = 2, then x = ?اگر x + y = 6, x − y = 2 تو x = ?
(a) 4(b) 2(c) 6(d) 8
Ans: (a) Add the equations: 2x = 8, so x = 4.
9.
In arithmetic sequence of a = 5 and d = 3 the a6 is:اگر جمعی سلسلے میں a = 5 اور d = 3 ہو تو a6 ہوگا:
(a) 18(b) 20(c) 22(d) 24
Ans: (b) a6 = a + 5d = 5 + 15 = 20.
10.
Missing value of the sequence 1,2,4,7,—,—,221,2,4,7,—,—,22 کی نامعلوم قیمتیں ہیں:
Instructions: Attempt any 10 Questions. Each Question carry 3 Marks.کوئی سے دس سوالات کے جوابات دیں۔ ہر سوال کے 3 نمبر ہیں۔
Q.1.
The sum of two number is 5 and their difference is 1 Find the number.دو اعداد کا مجموعہ 5 ہے اور ان کا فرق 1 ہے۔ اعداد معلوم کریں۔
Let the numbers be x and y: x + y = 5 and x − y = 1. Adding: 2x = 6 ⇒ x = 3, so y = 2. The numbers are 3 and 2.
Q.2.
What is the difference between finite and infinite sequence?محدود اور لامحدود سلسلے کے درمیان فرق کیا ہے؟
Finite sequence: has a limited number of terms (a last term), e.g. 2, 4, 6, 8, 10. Infinite sequence: goes on forever with no last term, e.g. 2, 4, 6, 8, …
Define arithmetic sequence.جمعی سلسلے کی تعریف کریں۔
A sequence in which the difference between any two consecutive terms is always the same (constant) is called an arithmetic sequence, e.g. 3, 7, 11, 15, … (common difference d = 4).
The sum of two polynomials is x²+2x−y². If one polynomial is x²−2xy+3, then find the other polynomial.دو کثیر رقمیوں کا مجموعہ x² + 2x − y² ہے۔ اگر ایک کثیر رقمی x² − 2xy + 3 ہو تو دوسری کثیر رقمی معلوم کریں۔
x−4/y−8 = y8/x4 (a negative power moves to the other side of the fraction line) = y8x4.
Total Marks: 30کل نمبر :30
Section-III (Constructed Response Questions)سیکشن III (انشائیہ سوالات)
Total Time: 1 hour 45 minutesکل وقت : 1 گھنٹہ 45 منٹ
Attempt any three Questions. Each Question carry 10 Marks.کوئی سے تین سوالات حل کریں۔ ہر سوال کے 10 نمبر ہیں۔
Q.3
(a) If A = h2(a + b), make h the object of the formula. Also find h when a = 4, b = 8 and A = 24. (5)اگر A = h2(a + b) ہو تو h کو فارمولے کا موضوع بنائیں۔ h کی قیمت بھی معلوم کریں جب a = 4، b = 8 اور A = 24 ہو۔
A = (h/2)(a + b) ⇒ 2A = h(a + b) ⇒ h = 2Aa + b.
Put A = 24, a = 4, b = 8: h = (2 × 24)/(4 + 8) = 48/12 = 4.
(b) Find solution set by elimination method. (5)حذف کے طریقے سے حل سیٹ معلوم کریں۔
x − 4y = 44x − y = 16
(The right side of the second equation is partly hidden in the scan; 16 is assumed.)
x − 4y = 4 …(1) 4x − y = 16 …(2). Multiply (1) by 4: 4x − 16y = 16 …(3). Subtract (3) from (2): 15y = 0 ⇒ y = 0. Then x = 4. Solution set = {(4, 0)}.
Q. No.4
(a) If x − 1x = 2, then find the value of x3 − 1x3. (5)اگر x − 1x = 2 ہو تو x3 − 1x3 کی قیمت معلوم کریں۔
(b) For what value of p the polynomial 3x3−7x2−9x+p becomes exactly divisible by x − 3? (5)p کی کس قیمت کے لیے کثیر رقمی 3x3 − 7x2 − 9x + p کو x − 3 پورا پورا تقسیم کرتا ہے؟
By the remainder theorem, put x = 3 and equate to 0: 3(27) − 7(9) − 9(3) + p = 0 ⇒ 81 − 63 − 27 + p = 0 ⇒ −9 + p = 0 ⇒ p = 9.
Q. No.5
(a) Subtract 4x + 6 − 2x2 from the sum of x3 + x2 − 2x and 2x3 + 3x − 7 (5)x3 + x2 − 2x اور 2x3 + 3x − 7 کے مجموعہ میں سے 4x + 6 − 2x2 کو منفی کریں۔
(b) If P = x2 − yz, Q = y2 − xz and R = z2 − xy, then find PQ, QR, PR and PQR. (5)اگر P = x2 − yz، Q = y2 − xz اور R = z2 − xy تو PQ، QR، PR اور PQR معلوم کریں۔
(a) Find the next two terms. 12, 14, 17, 21, ______ , ______اگلی دو رقوم معلوم کریں۔
Differences: 2, 3, 4, … (increasing by 1), so the next differences are 5 and 6: 21 + 5 = 26 and 26 + 6 = 32. Next two terms: 26, 32.
(b) Factorize the following: (5)درج ذیل کی تجزی کریں۔
(i) 3xy + 6x2y2 + 9xz(ii) 25x2 + 88xy + 64y2
(i) Take 3x common: 3x(y + 2xy2 + 3z).
(ii) 25x2 + 88xy + 64y2 does not factorize over integers as printed (the middle term of a perfect square (5x + 8y)2 would be 80xy, not 88xy). Splitting the middle term needs two numbers with product 25 × 64 = 1600 and sum 88, and none exist. If the question meant 80xy, the answer is (5x + 8y)2.
